OK, I give up now.  After a week of back and forth with an open ticket, I've come to the conclusion that whilst there is a way to do what I want, LP support is not going to assist.  Yes, I am frustrated and yes, I've noted that in my open ticket.  Just to vent, below is a sample of the responses I've received on this ticket.

"If they are working on 2 accounts on the same server it should be a difference in server configuration and I suspect it may be related to the file name."  [ presumably NOT a difference in server configuration, since the two accounts are on the same server.

I then asked : "I therefore have a question which needs a simple YES or NO response ... is it possible to upload root.war only and have Resin expand that as it does with other WAR files?"

The response: "We really apologize for the inconvenience. I was able to extra .war file. Please only put one root.war file, either in cap or in lower case."  This was followed by

root@happy [/home/lcgrr0/public_html/webapps]# jar xvf root.war 

presumably an indication that a shell command is needed to manually extract info.  Not helpful if one doesn't have shell access.

I asked : "1) Is it possible and permitted on the Lunarpages servers to upload a .war file and access the content using a simple Uniform Resource Locator (like http://www.lcgrr.org) without a path (like ../foobar)? 2) If it is possible, please confirm the exact name of the .war file to be used (root.war, ROOT.war, something else)?"

The response: "We really apologize for the inconvenience. I have checked that your ROOT.war file is not deploying in any resin 3.x based server, Where test .war file is extracting very easily. For Resin packaging/deployment I advise you to visit http://www.caucho.com/resin/admin/deploy.xtp" Yes, I knew that.  The URL is a reference to the Caucho Resin 4.x help pages, also no help!

"Regarding your questions .1 , Yes You can deploy in document root. Your ROOT.war if not extracting by Resin Servants. Please check with the link iI given you above and let us know if that helps."  It didn't.  Partially because the response wasn't understandable. What about question 2?

And to close, the message ended "If you have any questions, please don't hesitate to ask us, we will be happy to answer them. Please feel free to contact us for further help. We are committed to making your hosting experiences pleasant and fulfilling.

Seriously, boilerplate platitudes aren't so helpful.  This experience has been neither pleasant nor fulfilling.

There, I feel better now.  Not that I expect a response, given the liveliness of this forum, but you never know.  If anyone does know the secret of how to deploy a WAR file that is accessible without a path suffix to the URL, I'd be pleased to hear it.

Thanks.

Update - "... your domain's configuration entry in the global resin.conf file [that] was modified".

Ha!  Getting closer to the er, root cause!!

Sounds like you are getting somewhere. Hang in there.

@SkillAdvance. 
I had the same experience with a basic servlet exception http://www.lunarforums.com/jsp_and_servlets_support/servletexception-t55878.0.html.  I shared your exact notion that front support should not need to get involved in the deep techy stuff, they are there to inform people what .HTML files are used for   .    And yes the second line support seems to brush things off a bit too easy.   My guess is that 99.99% of technical programming issues are with the specific programmer's application code, not with LP setup.  And for them they can't tell them apart without tearing through code, so I kind of understand their viewpoint.  Those of us that experience the 0.001% of problems that are LP initiated will be in a world of hurt.   I understand this, but man it did not make my frustrations any easier that's for sure.

One problem, I dare say, is not with Lunar Pages support rather people that post in forums.  Most people that post in forums, do not go back for a final post, and put in the solution.  You have figured this out, your posts are good, and helpful, I've seen a few.  I figured it  out as well, however, I've done my share of dangling threads.

When the sky is falling, everyone runs to the forums.  They post their problems, ask people to help, then when the solution is found they don't return the helpful favour.  That's like getting to watch a whodunnit movie but never getting to see the last 10 minutes of the film.  Crazy.

Keep up the good work SkillAdvance.